We show that three-dimensional "sliding" analogs of the Kosterlitz-Thouless
phase, in stacked classical two-dimensional XY models and quantum systems
of coupled Luttinger liquids, can be enlarged by the application of a paral
lel magnetic field, which has the effect of increasing the scaling dimensio
ns of the most relevant operators that can perturb the critical sliding pha
ses. Within our renormalization-group analysis, we also find that for the c
ase of coupled Luttinger liquids, this effect is interleaved with the onset
of the integer quantum Hall effect for weak interactions and fields. We co
mment on experimental implications for a conjectured smectic metal phase in
the cuprates.